Answer: 6.2 m/s
Explanation:
1) This situation involves projectile motion, which follows a parabolic path.
2) Velocity components:
i) Initial velocity is denoted as V₀.
ii) Horizontal velocity component:
V₀x = V₀ cos α
Since horizontal velocity remains constant, Vx equals V₀x.
iii) Vertical velocity component:
V₀y = V₀ sin α
Its change over time is affected by acceleration due to gravity, g ≈ 9.8 m/s².
Vy = V₀y - gt = V₀ sin α - gt
3) Formulas for displacement:
i) Horizontal displacement:
x = V₀ cosα × t
ii) Vertical displacement:
y = V₀ sin α × t - (1/2) g t²
or y ≈ V₀ sin α × t - 4.9 t²
4) Working out the solution:
i) We know x = V₀ cos(32°) t = 2.00 m, because the salmon begins 2.00 m away from the waterfall.
Thus, V₀ = 2 / [cos(32°) × t]
ii) For vertical displacement: y = V₀ sin(32°) t - 4.9 t²
iii) Substituting V₀, y = sin(32°) × 2 / [cos(32°) × t] × t - 4.9 t² = 2 tan(32°) - 4.9 t²
iv) Setting y = 0.55 m (the height of the waterfall) to solve for t:
0.55 = 2 tan(32°) - 4.9 t²
t² = [2 tan(32°) - 0.55] / 4.9 = 0.143 s²
t = √0.143 ≈ 0.38 s
v) Finally, compute V₀:
V₀ = 2 / [cos(32°) × 0.38] = 6.2 m/s
